\section{Mechanical accuracy of the jigging}

\subsection{Intrinsic precision}

\subsubsection{The 'Frascati' combs}


   The precision combs holding the tubeplugs at the HV and RO ends
during the glueing of a tubelayer were assembled at Frascati.
They consist of 4 aluminum pieces with glued steel precision rods
to position the plugs.
These pieces were produced using a master jig
as descibed in [ref.Frascati], and then glued together to
make one 72 tube BOL jig.
  The assembled combs were measured on a CNC machine at NIKHEF.
The analysis of the measurements showed :

   . the average z-pitch of the two complete combs is 35.0355mm  
     at 20.4 +- 0.4 degC
     and deviations of < 0.1 \mum from this value  
     for the average z-pitch of the original jig pieces. 

   .  The  rms of the individual  z  positions 
     and the rms of the  y-deviations from a straight line 
     are less than  2\mum.
     No significant systematic shifts in z or y were found
     at the glue joints of the 4 pieces.



\subsubsection{The Tube combs}


The combs supporting the tubes inbetween the precision combs
at 0.5m intervals ,have been machined at NIKHEF as solid aluminum pieces
with a width corresponding to 18 tubes.A total of 50 pieces were produced
en measured on the CNC.

 To assemble the 9 full width combs (72 tubes) 
the 36 best pieces were selected, taking into account
the precision of the wedges and the connecting surfaces.
The connections between the pieces were checked with the RASNIK malmonitor
device prior to their fixation.

The assembled combs were again measured on the CNC and the results were 
compared with the nominal height and Frascati pitch.
The  RMS deviations of the tube positions  are less than 15\mum in z and y.

\subsubsection{The Sphere towers}

The sphere towers consist of a base block, one of 3 different
type of stacking blocks to adjust the spacer position  according to 
the type of layer to be glued,
and a top block with the sphere holder.  

Measurements with the CNC machine of all the separate parts allowed
a selection of optimal combinations of
base, stacking  and holder blocks resulting in a Y and Z accuracy
of   about 5um.


\subsection{Positionning of the mechanics on the table}

The accuracy of the $Y$ position of the mechanics is limited by 
the flatness of the granite table. Over short distances (one meter) 
this accuracy is about 10~\um. Over longer distances, 
temperature gradients start to play a role, 
which make the table bend and can lead to a sagitta of 20~\um over five meter.

The combs and towers are  initially positionned with low accuracy. 
The high precision is reached by adjustments and 
many remeasurements in an iterative way.

Both the precision and tube combs are positionned on the table
with a sliding fixation  such that 
they are allowed to expand freely in the direction away 
from the reference bar in case of temperature variations.
This was checked with laser interferometer measurements
and local heating of some combs with approximately +5 deg
temperature increase.



\subsubsection{ Frascati comb positioning}

 In order to properly combine the Frascati combs with tube combs
  a 20\mum steel foil was used to shim the height
 of the Frascati combs on the assembly table. This was needed
 due to a small change in the tube and plug geometry after
 the combs were already machined. 


   The relative height  above the table surface  of the precision wedges
was checked several times before and during chamber construction
with SLOF measurements. Average deviations from the nominal value
were found to be less than 5\mum with an rms of < 4\mum 
for different positions along the combs. 

The relative torque of the Frascati combs is measured by using tiltmeters.
 Despite the high intrinsic precision precison of these tiltmeters,
 a measurement better than than 10~\urad seems impossible. We measured the
torque to be zero whithin the scatter of the measurements.



The X distance was based on a test-TUBE with known length
and rechecked by tape-measure. The X-distance between the tube supports is
 stable within 500~\um, dominated by the low precision of the X coordinate of these supports themselves.

Most important is the angle between the two Frascati combs, related to $A_Y$.
Therefore a laser beam in the $X$ direction is used, aligned by the silicon sensor on the first wedges of the Frascati combs. 
Using a penta prism, accurate to 10~\urad, the laserbeam is reflected over
 an angle of 90 degrees into the $Z$ direction.
The Frascati combs are aligned with respect to this beam, leading to a
 straigthness in $X$ within 100~\um. 
Thus, seen in the $X$-$Z$ plane, the Frascati combs describe a rectangular 
shape with angular deviations of about 100~\urad.


\subsubsection{ Tube comb positioning}




 The tube combs are positionned on the assembly table with one side fixed
to a reference bar. Each jig position is adjusted in z such that
the tube positions of the 9 combs deviate less than 50\mum from straight lines 
connecting the two precision combs at each end of the table.

 For this we used a laser and silicon-sensor combination [ref SiSens/Munich]
 The laser beam defines a straight line between the two precison combs 
 roughly along path of  a tube. The relative beam position
 in z and y is measured by placing a silicon sensor with strips in
 both directions with a pitch of 400\mum in the beam. The sensor
 is mounted on a brass support with steel inserts which are positionned
 on small steel rods lying in the wedges of the combs. The sensor
 is placed succesively on each of the 11 combs along the beam.
 The centre of gravity of the beam profile is determined in both
 z and y for each measurement. A line is defined by the two measurements
 of the precision combs and the deviations from that line are calculated
 for the tube combs inbetween. These measurements are repeated at 
 several positions along the precision combs.
  In fig [sisens] we show the distribution of the deviations for
 some of the measurements. The rms of the deviations is typically
 xx \mum in z and yy \mum in y, thus amply fulfilling the requirement
 of 100 \mum rms for the centrisity of the wire with respect to
 the tube centre. These measurements will be  repeated regularly
 as part of the QA/QC procedure.


  SLOF measurements directly comparing  the relative height of corresponding
wedges in the Frascati combs and in the tube combs next to them
showed deviations less than 20\mum from the nominal value. 
This ensures that the alignment platforms
which are glued onto the first tubelayer in this area can be positionned with 
with sufficient precision.


\subsubsection{ Sphere tower positioning}
The sphere towers will support the spacer during the gluing procedure and
so determine the wire positions between the several tube layers.
The towers are initially positioned  with an accuracy 
in the $Z$ direction of about 100~\um using standard optical tools. 

The alignement in $Y$ of the three refence towers is checked with
 the silicon sensor.
The results indicate that the middle tower with respect
 to a line defined by the $Y$ of the outer towers deviates by 
 -25~$\pm$~10~\um. The non
 reference side is checked in a similar way, which reveals the same deviation.
The intrinsic accuracy of these towers is does not allow such deviation,
 leading to the conclusion that the surface of the granite table, 
at the position of the towers, has deviations of the same order. We tried
to find more evidence, but to measure with this accuracy over 5~m is far from
trivial. However, (re)measurements with standard optical tools indeed
 suggest a negative deviation in heigth of the central towers.



   On the reference side of the table the sphere  towers are fixed to 
the corresponding  Frascati combs.
In order to assure
that the two multilayers are glued to the spacer without a 
significant stereo angle between them, the distance between the wedges
and the spacer fixation in z must differ by less than 10\mum
for the two precision combs. This is because the HV and RO
ends of a chamber are interchanged with respect to the two
precision combs for glueing either of the two multilayers
(see [Assembly.intro]).
 For the QA/QC of this requirement we use an auxiliary device
called the BOL-monitor. 

This consists of a cross-plate
with two small lenses attached to one of the flanges
 approximately 1.8m away from each other.
at positions corresponding to two precision wedges in the combs.
This cross-plate is positionned on the stacking towers in the
same way it is done for glueing tube layers. The relative
position of each of the lenses is measured with an Mask/CCD-camera
combination  mounted on a brass fork with steel positionning inserts.
 This fork is placed on two precise steel rods 
lying in the jig wedges such that
the cross plate lens is  hanging aproximately in the middle between the
Mask and the CCD. With the thus created RASNIK system the 
the lens position in Z and Y is read out , while varying
the fork position by +-2mm in the optical axis direction (X)
along the supporting rods. These measurements are done 
at both precision combs, using the same fork/rods combination.
Comparison of the measurements yields the difference in Z
and Y of the jig and reference assembly tower combinations.
The use of two lenses on the cross-plate 
provides two independent measurements. In addition
the whole procedure is repeated with the cross-plate rotated
180 degrees around the vertical axis, thereby interchanging
the lens/fork combinations and yielding additional redundancy.
  The BOL-monitor was used to fix the initial position of
the towers and the measurements will be repeated regularly as part of
the QA/QC procedures.

  An recent example of such a measurement is shown in fig [xyzbol11.ps].
 Here we plot the difference in Z and Y position of the cross plate
 lenses with respect to the two precision combs, as measured on the North 
 and South side of the assembly table. The position difference is plotted
 as function of the X position of the forks; X=0 corresponding to the
 lens being in the middle between the mask and the CCD of
 of the Rasnik system.
 The X values are derived from magnification of the mask image
 on the CCD.
  Straight lines are fit through the two corresponding sets of data 
 at the North and South side respectively. 
 The points show the deviations of the measurements on the North side
 from the line fit throught the measurements on the South side, and
 vice versa.
 The two colors differentiate between the two orientations of 
 the monitor cross-plate, which in principle
 should lead to the same result. The corresponding lens positions are
 indicated by Reference side and NonReference side. 
 For the DZ measurement the the Reference side data are the most reliable,
 as the distance between the reference tower and the lens is short (30 cm)
 and temperature effects can be neglected. For the Non-Ref Z measurements
 the lens is at 210 cm from the reference tower and its position is thus
 subject to temperature differences of the cross-plate and 
 the combs between North
 and South data sets, which are not corrected for.
 For the DY measurements the temperature effects can be neglected .

    From the plot one can see that with both orientations of the cross-plate
 we measure at the Ref side a difference  in Z of  6\mum,
 which is within the 10\mum tolerance.
  This value has remained the same within $\pm$5\mum over 2 years since
 the comb positions were fixed.
 
  The Y differences are much less critical for the chamber assembly,
 since the glueing procedure assures that the distance between the two
 multilayers remains the same on both ends of a chamber and only the
 relative position of the cross-plates glued between them is affected.
 Nevertheless the measurements show that Y differences are smaller than
 20\mum on both Ref and NonRef side of the combs.


 



























